Abstract
In this paper for constructing of a class of functions consisting of integral representations, we introduce a double integral, a formula pertaining to extended fractal strings, consisting of separate variables functions in the integrand. Further by this double integral formula, we determine various functions, integrals and contour integral representations on introducing different special functions for these integrand functions connecting to RiemannLiouville and Weyl fractional integral functions. Finally, we apply our obtained results to find certain boundary value problems and present precise examples.
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